Problem Name

Problem Description

Notes

derivative_21

Find a formula for the derivative with respect to x for the function. (Treat a, b, and c as constants.)
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derivative_22

Find a formula for the derivative with respect to x for the function. (Treat a, b, and c as constants.)
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derivative_23

Find a formula for the derivative with respect to x for the function. (Treat a, b, and c as constants.)
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derivative_24

Find a formula for the derivative with respect to x for the function. (Treat a, b, and c as constants.)
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derivative_25

If , where is a constant and is a function of , then use the definition of the derivative to prove that .

derivative_26

Write an expression for for the function . ( ). Then use the definition of the derivative to find .

derivative_27

Using the definition of the derivative, show that, if , then .

derivative_28

Find the values of where the slope of the curve is equal to 3.

derivative_29

For what values of is the line tangent to the curve ?

derivative_30

Newton's method provides an iterative method for estimating the x-intercept of complicated functions. The goal of the method is to find such that . First, make a guess ( ) that is reasonably close to the true value of . Then calculate a better guess according to the formula . The method can be repeated to yield a still better guess, . Keep going until you are satisfied that the result is close enough to the true answer. Now, use Newton's method to estimate the cube root of 7. Start with , and find the x-intercept of the function . Perform a total of 3 iterations and compare with a calculator value.